M2510971 Mersenne number exponent details

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M2510971

<<<

>>>

is 2 ^2510971 - 1

has 755878 decimal digits

takes 0.174 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	F2E247C1262DB1D1	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	23.7378	67.6471%	3200000	112000000	0.9180	8.0607%	24.6558	70.2549%	2.6079%
PrimeNet	2⁵⁹	0.0306	62.7119%	11000	190000	0.0021	2.6412%	0.0327	63.6967%	0.9848%
GPU72	2⁶³	0.6356	65.0794%	11000	170000	0.0020	1.4087%	0.6376	65.5713%	0.4919%
Difference	+5	+23.1022	+2.5677%	+3189000	+111830000	+0.9160	+6.6519%	+24.0182	+4.6836%	+4.6836%

Known prime factors (1 factor, 74.8 bits, 0.00297810% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2510971	32419826937891805988791	23	74.779	6455635476851745 3² × 5 × 19 × 31 × 243562930649	2020-05-13	31	243562930649	1,914.5	1,334.6	2,492.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.235%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	236250		-		-	-	0.003	-	-	0.795%
2010-12-16T22:40:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.264%
2011-01-01T00:57:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.365%
2011-01-04T22:09:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.529%
2011-10-04T06:11:00	markr	tiny	165000	3918750		-		-	-	0.037	-	-	3.099%
2016-02-24T02:11:39	mikr	MSI	3200000	112000000	12	-		-	-	0.918	-	-	8.061%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2016-02-23T16:29:15	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.031	-	-
2009-01-30T20:20:00	Sturle Sunde	giny.ifi	2⁶⁰	2⁶¹		-	-	0.061	-	-
2012-06-12T20:31:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.122	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.391	-	-
2015-02-18T11:36:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.782	-	-
2015-02-18T11:36:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.488	-	-
2015-11-05T09:47:21	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.976	-	-
2017-07-31T07:56:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.952	-	-
2019-05-13T13:38:13	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.90	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.128 GHz-days
Estimated T-Level:	1.700

Digits	B1	Curves	Complete	FacMiss
20	11000	34 / 100	0.340	71.055%
25	50000	34 / 280	0.121	88.546%

New Calculation Method

Total ECM effort:	3.128 GHz-days
Estimated T-Level:	1.700

Digits	B1	Complete	FacMiss
20	11000	1.097	33.395%
25	50000	0.099	90.563%
30	250000	0.006	99.391%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	3.036
50000	5000000	32419826937891805988791	1	0.092

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-25T14:45:00	Lupo	yorick	50000	5000000						3	0.276
2010-04-11T02:49:00	Lupo	yorick	50000	5000000						3	0.276
2012-08-25T16:08:00	Bud	annan	50000	5000000						3	0.276
2014-03-09T08:21:00	he4var		50000	5000000						3	0.276
2015-07-29T00:16:00	guru	w1	50000	5000000						3	0.276
2016-02-29T07:51:59	arnaud	CHAMOT09	50000	5000000						3	0.276
2016-07-02T21:01:48	Bruce	test	50000	5000000						3	0.276
2017-04-10T14:38:26	deo2016	deo2016.home.new	50000	5000000						3	0.276
2017-09-05T09:27:40	Sebastian Hornbostel	V2	50000	5000000						3	0.276
2018-01-10T12:36:46	storm5510	Athlon2x4	50000	5000000						3	0.276
2018-09-23T19:18:50	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2020-05-13T08:36:46	daveward2005	MW	50000	5000000	32419826937891805988791	74.779	1	2		1	0.092

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	F2E247C1262DB1D1	0.174
2018-06-04T07:17:40	kkmrkkblmbrbk	old	F2E247C1262DB1D1	0.174

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-05-13T12:31:28

CrypticClue

cruncher

32419826937891805988791

CFB3548DED8CEF1A

2020-05-13T13:11:08

ATH

ec2-PRPCFDC

32419826937891805988791

CFB3548DED8CEF1A

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 3200000, B2 = 112000000 (P-1 stage 2)

B1 = 3200000 (P-1 stage 1)

B1 = 165000, B2 = 3918750 (P-1 stage 2)

B1 = 165000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 236250 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-05-13T13:11:08+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront